On relationship between two ancient Chinese algorithms and their application to flash evaporation

This paper gives a brief introduction to two ancient Chinese methods, Ying Buzu Shu and He Chengtian average. Their relationship is revealed, and it is proved that the two methods are equivalent under some special cases, that means He Chengtian average can be derived from the method of Ying Buzu Shu. Rachford-Rice equation arising in flash evaporation is used as an example for their simple application.